On the probabilistic time-dependent axial shortening of tall concrete buildings

Tall concrete buildings experience time-dependent axial shortening which may be interpreted as either absolute or differential, the former being with respect to a single column or core element, the latter being with respect to adjacent elements. The types of analyses undertaken to determine axial shortening would normally be deterministic, the rigour being commensurate with the degree of shortening likely to be experienced. Mathematical rigour, however, may or may not be justified in the context of the natural variability of constituent parameters and thus a closer examination of the probabilistic uncertainties associated with axial shortening, particularly for tall buildings, is warranted. Shortening is influenced by, amongst other things, the complex load history of a building during its construction cycle. In this context the properties of concrete are investigated to determine those that are critical to any axial shortening analysis. The work here describes three probabilistic techniques, namely, Monte Carlo simulation, and first- and secondorder moment analyses. Each incorporates random constitutive information in addition to a rigorous procedure for obtaining the representative shortening values. Element behaviour is modelled by the composite models of either Faber, Trost and Bazant, Dischinger or improved Dischinger, combined with the recommendations of the ACI, CEB-FIP, AS-3600 and other sources for describing creep and shrinkage. These models are coupled with the detailed load history of each successive element, based on the construction sequence of the building, and the usual environmental effects, resulting in a procedure capable of analysing fully the axial shortening effects to a high level of detail and with a measured degree of certainty. A software program has been developed to do this analysis. The probabilistic distributions of axial shortening results are subsequently determined using standard goodness of fit tests. With numerous predictive methods available for column behaviour, the author sets out to examine their differences in the context of axial shortening behaviour. An assessment of the sensitivity of each input parameter, in addition to comparisons with other predictive procedures is made. Conclusions follow from these studies. Finally, the probabilistic models are, to a limited extent, compared to field data of column shortenings.